The Swansea City defender had been heavily tipped to succeed Jamie Carragher at the heart of the Anfield club's back line next season, with the veteran centre-back set to hang up his boots, but Fenway Sports Group has no plans to rubber-stamp any deal.

Rodgers has vowed to "search far and wide" for Carragher's replacement but, while the 40-year-old continues to hold Williams in high esteem from his time at the Liberty Stadium, it is not a view shared by the Reds' transfer committee, which assesses and identifies transfer targets.

FSG's previous management structure saw them fail to broker a deal for Clint Dempsey last summer, with the attacking midfielder's move to Tottenham on transfer deadline day forcing Rodgers to rely heavily on Luis Suarez until January as one of Liverpool's only two recognised senior strikers.

Williams, who agreed a one-year extension to his current Swansea deal to stay with the Capital One Cup holders until 2015, is valued at £12 million, which the Anfield hierarchy do not believe represents good business sense due to the lack of longevity his capture would provide.

However, Goal.com understands that the Americans' reluctance to bankroll a move for the boyhood Liverpool fan does not rule out future moves for experienced players, should they become available at a reasonable price.

Williams's representatives met with Arsenal in London in April as the Gunners began formalising their plans to strengthen their central defence this season, while Laurent Koscielny has been targeted by Bayern Munich, as Goal.com exclusively revealed on Thursday.